Fredholmness and finite section method for Toeplitz operators in $l^p(Z_{+}\times Z_{+})$ with piecewise continuous symbols II

Abstract

In this paper we prove sufficient conditions for Fredholmness of discrete Toeplitz operators with piecewise continuous symbols on the space $l^p$ over the quarter-plane and for the applicability of the finite section method to such operators. The methods used here are based on a bilocalization technique and the local principle of Douglas and Krupnik. Part I of this work contained the proofs of the necessity of the corresponding conditions, the necessary definitions, and the formulation of the main results.